Math Is Fun Forum

666 bro

Member

From: Flatland

Registered: 2019-04-26

Posts: 706

Visualizing proof

How could we visualize the proof (limx→0 sin(x)/x)  ?

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"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Visualizing proof

hi

Here's the proof that I was taught many years ago.

Draw a circle radius R and centre C.  Mark points A and B as shown and D so that AD is perpendicular to CB.

Let angle ACB be x in radians.

sin(x) = AD / R

arc length AB / whole circumference = arcAB / 2.pi.R = angle of arc / whole circle angle = x / 2.pi

cancelling the 2.pi gives arcAB / R = x

So sin(x) / x = AD / arcAB

implies sin(x) < x but as x approaches zero AD approaches arcAB so sin(x) / x tends to 1.

Bob

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Children are not defined by school ...........The Fonz
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